Classification of microtubule histories

A microtubule of a given length undergoes all possible scenarios of transitions between growing and shrinking phases, so-called microtubule dynamic instability. In this Paper we utilize a minimal two-state model proposed by Kill [Proc. Natl. Acad. Sci. USA 81, 6728 (1984)] that is equivalent to a two-state random walk. Using a technique for classifying discrete random walk configurations by introducing a counting variable in evolution equations, we have derived expressions for probability densities (which contain information about all transition histories) of phase transitions before the complete disappearance of a microtubule. As a result, the mean lifetime of a microtubule turns out to be equal to the total lifetime of growing and shrinking phases times the average number of transitions. An attractive feature of this simple model is that elementary formulas relating statistical averages to rate parameters are obtained. [S1063-651X(99)02001-2].